# Concept of Stress Strain Curve For Mild Steel

Generally mild steel rods are highly preferred for many construction purposes. As it has high tensile strength when used with concrete, knowing the behavior of mild steel rod under loading helps in choosing for better use. This behavior of a mild steel rod under loading can be analyzed using stress strain curve for mild steel rod.

The stress strain curve for mild steel consists of strain along the x-axis and stress along the y-axis. Stress strain curve for mild steel consists of various stages such as

• Proportional Limit.
• Elastic Limit.
• Upper Yield.
• Lower Yield.
• Ultimate Stress.
• Breaking Point.

If the stress is applied gradually to a mild steel rod, the strain also gradually increased that is represented in point ‘A’ In this stage when stress is removed from the rod the strain returns to ‘0’. Thus the ‘0’ to ‘A’ points is called as proportional limit.

In this limit the stress is directly proportional to strain { σ ∝ e }, that means the steel rod obeys ‘Hooke’s law’. In this stage the proportionality is expressed as ‘E’, thus

$\sigma= E. e$

$E = \frac{\sigma }{e}$

Here, E = Young’s modulus or modulus of elasticity.

Thus Young’s modulus is defined as the ratio of stress to a strain of the mild steel rod. The unit of young’s modulus is N/mm².

The increase of stress to the point ‘B’, the strain also increased proportionally it is called as elastic limit. In this stage, if the applied stress is removed the strain returns to an original position that is rod gains to original shape. The stress increased beyond the elastic limit, the material undergoes deformation. Which means the permanent extension occurs and the mild steel rod does not regain its original shape even after the stress is removed. This is expressed as ‘C’ to ‘D’ point in the graph which is called as yield point.

In Point ‘C’ at which maximum stress is required for a rod to undergo deformation is called as upper yield point. In point ‘D’ of which minimum stress is required for a rod to undergo deformation is called as lower yield point. The increase of stress beyond this limit increases strain gradually to a point. This point is ‘E’ which is called as ultimate stress or ultimate strength point. Ultimate stress is the maximum stress the rod can withstand, thus this portion is called a strain hardening.

Further increase of stress beyond the ultimate stress, the localized reduction occurs in the cross sectional area of the rod which is the weakest point of the material. This is called as necking stage that means a breaking point stage. At this stage the mild steel rod breaks, thus the curve drops to the point ‘F’. Resultant curve obtained is the stress strain curve for mild steel rod.

Under the action of load the point ‘A’ to ‘B’ is elastic region and point ‘B’ to ‘F’ is the plastic region of mild steel rod. Similarly if you plot the stress strain curve for any material you can determine the yield strength, ultimate strength and the breaking point of the material.